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Several devices exhibiting memory effects have shown up in nonlinear circuit theory in recent years. Among others, these circuit elements include Chua's memristors, as well as memcapacitors and meminductors. These and other related devices…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
The electric current as the flux of current density -- a signed scalar, not a vector -- is inconsistent with the concept of the current direction, commonly invoked in the electric circuit analyses within, for example, Kirchhoff's current…
This paper serves as a starting point for machine learning researchers, engineers and students who are interested in but not yet familiar with causal inference. We start by laying out an important set of assumptions that are collectively…
This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can…
Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one…
Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…
We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to…
Interface circuits are the key components that enable the hybrid integration of superconductor and semiconductor digital electronics. The design requirements of superconductor-semiconductor interface circuits vary depending on the…
We study current fluctuations in tunnel junctions driven by a voltage source. The voltage is applied to the tunneling element via an impedance providing an electromagnetic environment of the junction. We use circuit theory to relate the…
Despite the excelling performance of machine learning models, understanding their decisions remains a long-standing goal. Although commonly used attribution methods from explainable AI attempt to address this issue, they typically rely on…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal…
A totally asymmetric exclusion process consisting of classical particles with next-nearest-neighbor interactions has been considered on a 1D discrete lattice with a ring geometry. Using large deviation techniques, we have investigated…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
We consider the problem of classifying trajectories generated by dynamical systems. We investigate a model-based approach, the common approach in control engineering, and a data-driven approach based on Support Vector Machines, a popular…
The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…
In this paper we focus on concurrent processes built on synchronization by means of futures. This concept is an abstraction for processes based on a main execution thread but allowing to delay some computations. The structure of a general…
Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed…
While the standard formulation of quantum theory assumes a fixed background causal structure, one can relax this assumption within the so-called process matrix framework. Remarkably, some processes, termed causally nonseparable, are…